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International Master Program "Applied Mathematics and Stochastics"

Probability and Statistics

    Master Educational Programme “Probability and Statistics” is designed to teach both foreign students and graduates of the Russian higher education institutions. The main goal of this Progrqmme is to train highly qualified specialists who are able to solve new problems and to produce new knowledge in various fields of Probability Theory and Statistics, to apply probabilistic and statistical results in models arising in manufacturing and finance, in computer networks and quality control, in risk assessment and reliability.
    Probability is a core mathematical discipline, alongside geometry, algebra, and analysis. In recent years, the evident power and utility of probabilistic reasoning as a distinctive method of scientific inquiry has led to an explosive growth in the importance of probability theory in scientific research. Central to statistics and commonplace in physics, genetics, and information theory for many decades, the probabilistic approach to science has more recently become indispensable in many other disciplines, including finance, geosciences, medical sciences, artificial intelligence and communication networks. Probability and statistics are used to model uncertainty from a variety of sources, such as incomplete or simplified models. Statistical tools are at work in almost every area of life, including agriculture, business, engineering, medicine, law, regulation, and social policy, as well as in the physical, biological, and social sciences and even in parts of the academic humanities. Last decades the scope of probability theory and statistics increased with the emergence of new sub-fields such as queueing theory and renewal theory, nonparametric statistics, time series analysis, sequential analysis.
    In most of these areas deep results have been obtained by the leading researchers of Siberian probability school. The lecture courses of the Programme “Probability and Statistics” include the latest advances in all these areas.
    Programme includes courses on stochastic processes, random walks, risk theory, financial mathematics, martingales, regression analysis, applied statistical methods, Markov chains, multivariate limit theorems, asymptotic properties of functionals of order statistics, as well as on fundamentals of modern numerical methods theory and of modelling and simulation.
    The training period of the Master Programme “Probability and Statistics” in full-time education is 2 years. One academic year includes two semesters, two test and examination sessions. Training capacity within the Programme including all kinds of classroom and independent work, research student’s work and the time taken for quality control is 120 credits. One credit is equal to 36 academic hours. Training activities include research work in a laboratory of Probability and Mathematical Statistics of Sobolev Institute of Mathematics, conferences presentation, preparation of term papers, preparation and defense of Master Thesis.

Numerical Statistical Modelling

    This is a 2-year English-taught programme at the Master level. It is aimed at training and developing research skills in Numerical Modelling, Monte Carlo Methods and in their applications.
    The Programme is research-oriented. Each semester a student is supposed to devote a half of time to a research project, to be done at Institute of Computational Mathematics and Mathematical Geophysics. Results of this research project must be presented in a form of a Master Dissertation at the end of 2nd year of studies.
    Topics of lectures and research includes, but are not limited to
        –  numerical modelling of random values and processes,
        –  solution of ordinary and stochastic differential equations,
        –  theory of radiation transfer,
        –  stochastic simulation methods in applied mathematics, physics, meteorology, economics (including financial mathematics),
        –  discrete-stochastic numerical methods,
        –  modern computer technologies in stochastic simulation, etc.
    Lecture courses and research supervision are provided by professors of the Novosibirsk State University and leading researchers from institutes of the Russian Academy of Sciences. They all are members of the worldwide known scientific school on numerical stochastic simulation headed by Professor G.A.Mikhailov.

Inverse and Ill-Posed Problems: Theory, Numerics and Applications

    The main purpose and characteristic feature of this program is the accessibility of presentation and an attempt to cover the rapidly developing areas of the theory, numerical methods and applications of inverse and ill-posed problems as completely as possible.
    In direct problems of mathematical physics, researchers try to find exact or approximate functions that describe various physical phenomena such as the propagation of sound, heat, seismic waves, electromagnetic waves, etc. In these problems, the media properties (expressed by the equation coefficients) and the initial state of the process under study (in the nonstationary case) or its properties on the boundary (in the case of a bounded domain and/or in the stationary case) are assumed to be known. However, it is precisely the media properties that are often unknown. This leads to inverse problems, in which it is required to determine the equation coefficients from the information about the solution of the direct problem. Most of these problems are ill-posed (unstable with respect to measurement errors). At the same time, the unknown equation coefficients usually represent important media properties such as density, electrical conductivity, heat conductivity, etc. Solving inverse problems can also help to determine the location, shape, and structure of intrusions, defects, sources (of heat, waves, potential difference, pollution), and so on. Given such a wide variety of applications, it is no surprise that the theory and numerical methods of inverse and ill-posed problems has become one of the most rapidly developing areas of modern science. Today it is almost impossible to estimate the total number of scientific publications that directly or indirectly deal with inverse and ill-posed problems. However, since the theory, numerical methods are relatively young, there are many terms are still not well-established, many important results are still being discussed and attempts are being made to improve them. New approaches, concepts, theorems, methods, algorithms and practical problems are constantly emerging.
    Main topics:
        - Ill-Posed problem concept
        - Inverse problems classification
        - Regularization methods
        - Applications: Geophysics, Medicine, Biology, Finance, Social sciences, Big Data, Data Mining, Machine Learning, Image Processing.

Discrete Mathematics and Combinatorial Optimization

    During the last century the discrete and computational mathematics got boosting development which is connected mainly with the widespread involvement of computers and computer technologies into the everyday life. This required the development of new methods of studying, processing, transmitting, storing, protecting and analyzing the large volumes of information and also training the specialists knowing all these methods. A modern specialist in discrete mathematics and combinatorial optimization has to possess a deep knowledge of graph theory, scheduling theory, coding theory, cryptography, operations research, data analysis methods, mathematical modeling, linear, convex and integer programming, complexity theory, algorithms development and analysis, etc.
    The purpose of the Master Educational Programme "Discrete Mathematics and Combinatorial Optimization" is training highly qualified specialists in the following areas:
        –  Operations research
        –  Optimization methods
        –  Discrete analysis
        –  Graph theory
        –  Scheduling theory
        –  Coding theory
        –  Algorithms
        –  Data analysis.
Such specialists should be capable of working in research institutes, universities, programming firms, engineering companies, etc.
    The training is based on requirements of the State Educational Standard 01.04.02.